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Homological conditions for graphical splittings of antisocial graph groups

Lookup NU author(s): Dr Michael Batty

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Abstract

We define an antisocial graph group to be a graph group arising from a graph whose clique graph is triangle free. In every dimension, the existence of graphical splittings of an antisocial graph group G is shown to correspond to nonvanishing of Betti numbers of the ball of radius 1 in the well-known cube complex on which G acts freely. This can be regarded as a first step towards generalising Stallings' ends theorem to higher dimensions. (C) 2001 Elsevier Science B.V. All rights reserved.

Publication metadata

Author(s): Batty M

Publication type: Article

Publication status: Published

Journal: Topology and Its Applications

Year: 2002

Volume: 125

Issue: 3

Pages: 447-463

ISSN (print): 0166-8641

ISSN (electronic):

Publisher: Elsevier BV

URL: http://dx.doi.org/10.1016/S0166-8641(01)00290-5

DOI: 10.1016/S0166-8641(01)00290-5

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